The manufacturer of low-calorie dairy drink desires to compare taste appeal of new formula (formula B) with that of standard formula (formula A). Each of three judges is given three glasses in random order, two containing formula A and other containing formula B. Each judge is asked to state which glass he most enjoyed. Assume that two formulas are equally attractive. Let X be the number of judges stating a preference for the New formula (A).
a) List all the elements of the sample space (S).
b) Find the probabibility distribution for a random variable X.
c) What is the probability that at least two of the judges state a preference for formula A?
d) Find the expected value of a random variable X.
e) Find the standard deviation of a random variable X.